# Saturated liquid and vapour above triple point
T1 = numpy.linspace(iapws1995.Tt, iapws1995.Tc, 300)
hsat_liquid1 = iapws1992.hsat_liquid(T1)
hsat_vapor1 = iapws1992.hsat_vapor(T1)
# Saturated ice (below triple point)
T2 = numpy.linspace(150, iapws1995.Tt, 300)
psubl = iapws2011.psubl_ice_Ih(T2)
hsat_ice2 = iapws2006.h(T2, psubl)
# Saturated vapour below triple point
rhoest = psubl / (iapws1995.R * T2)
# pylint: disable=cell-var-from-loop
rho = numpy.array([
newton(lambda rho_: iapws1995.p(rho_, T_) - p_, rhoest_)
for p_, T_, rhoest_ in zip(psubl, T2, rhoest)
])
hsat_vapor2 = iapws1995.h(rho, T2)
## Plotting ##
fig = pyplot.figure(figsize=[4, 2.8])
fig.set_tight_layout(True)
pyplot.plot(T1, hsat_liquid1 / 1e6, 'k-', linewidth=1)
pyplot.plot(T1, hsat_vapor1 / 1e6, 'k-', linewidth=1)
pyplot.plot(T1[-1], iapws1995.hc / 1e6, 'ko', markersize=4)
pyplot.plot(T2, hsat_ice2 / 1e6, 'k-', linewidth=1)
pyplot.plot(T2, hsat_vapor2 / 1e6, 'k-', linewidth=1)
# Get the bounding temperatures for this isobar
Tmin = Tsat(p) if p < pc else TMIN
Tmax = TMAX
# Get the temperature series
T = numpy.linspace(Tmin, Tmax, 300)
# Estimate the minimum density
rhoest = p/(iapws1995.R*Tmax)
# Solve for the densities along the isobar, using the previous
# result as the next estimate
rho = []
for T_ in T[::-1]:
# pylint: disable=cell-var-from-loop, undefined-loop-variable
rho.append(newton(lambda rho_: iapws1995.p(rho_, T_)-p, rhoest))
rhoest = rho[-1]
rho = numpy.array(rho)[::-1]
# Get the entropies
s = iapws1995.s(rho, T)
# Save the arrays
ss.append(s)
Ts.append(T)
# Liquid phase
for i, p in enumerate(ps):
if p >= iapws1995.pc:
continue
# Parse command-line arguments
parser = argparse.ArgumentParser()
parser.add_argument('-o', dest='path')
path = parser.parse_args().path
## Calculations ##
# Define a series of temperatures
Tl = numpy.linspace(273.16, 373.15, 200)
# Determine the density at normal pressure for this series of temperatures.
# Use the liquid saturation density for each temperature as an estimate.
# pylint: disable=cell-var-from-loop
rhoest = iapws1992.rhosat_liquid(Tl)
rhol = numpy.array([
newton(lambda rho_: iapws1995.p(rho_, T_) - 101325, rhoest_)
for rhoest_, T_ in zip(rhoest, Tl)
])
vl = 1 / rhol
# Ice (solid) temperatures and volumes
Ts = numpy.linspace(-25, 0, 100) + 273.15
vs = 1 / iapws2006.rho(Ts, 101325)
## Plotting ##
fig = pyplot.figure(figsize=[4, 2.8])
fig.set_tight_layout(True)
# Isobar
# Parse command-line arguments
parser = argparse.ArgumentParser()
parser.add_argument('-o', dest='path')
path = parser.parse_args().path
## Calculations ##
# Define a series of temperatures
T = numpy.linspace(273.2, 373.15, 100)
# Determine the density at normal pressure for this series of temperatures.
# Use the liquid saturation density for each temperature as a first estimate.
# pylint: disable=cell-var-from-loop
rhoest = iapws1992.rhosat_liquid(T)
rho = numpy.array([newton(lambda rho_: iapws1995.p(rho_, T_) - 101325, rhoest_)
for rhoest_, T_ in zip(rhoest, T)])
# Get the heat capacities for these densities
cp = iapws1995.cp(rho, T)
## Plotting ##
fig = pyplot.figure(figsize=[4, 2.8])
fig.set_tight_layout(True)
pyplot.plot(T-273.15, cp, 'k-', linewidth=1)
pyplot.xlabel(r'Temperature ($\mathrm{^{\circ}C}$)')
pyplot.ylabel(r'Heat Capacity (J/K/kg)')
# Vaporization ----------
T1 = numpy.linspace(Tt, Tc, 300)
hsat_liquid1 = iapws1992.hsat_liquid(T1)
hsat_vapor1 = iapws1992.hsat_vapor(T1)
Lvap = hsat_vapor1 - hsat_liquid1
# Sublimation ----------
T2 = numpy.linspace(150, Tt, 300)
psubl = iapws2011.psubl_ice_Ih(T2)
hsat_ice2 = iapws2006.h(T2, psubl)
rhoest = psubl / (iapws1995.R * T2)
# pylint: disable=cell-var-from-loop
rho = numpy.array([newton(lambda rho_: iapws1995.p(rho_, T_) - p_, rhoest_) \
for p_, T_, rhoest_ in zip(psubl, T2, rhoest)])
hsat_vapor2 = iapws1995.h(rho, T2)
Lsub = hsat_vapor2 - hsat_ice2
# Fusion ----------
T3 = numpy.linspace(251.165, Tt, 300)
pmelt = iapws2011.pmelt_ice_Ih(T3)
hsat_ice3 = iapws2006.h(T3, pmelt)
# pylint: disable=cell-var-from-loop
rho = numpy.array([newton(lambda rho_: iapws1995.p(rho_, T_) - p_, 1000) \
for p_, T_ in zip(pmelt, T3)])
hsat_liquid3 = iapws1995.h(rho, T3)
Tc = iapws1995.Tc - 273.15 # C
Ts = numpy.array([-25, 0, 40, 100, 200, Tc, 1000, 2300]) + 273.15 # K
rhos = []
ps = []
# Determine the piecewise isotherms. Obtain the gas/vapor segments first,
# followed by the liquid and solid segments. We don't need to obtain data
# in the mixed phase region; the plateaus emerge when the segments are
# concatenated.
# Gas/vapor and supercritical fluid phases
for T in Ts:
# Determine the minimum density. Estimate it using the ideal gas law.
# pylint: disable=cell-var-from-loop
rhomin = newton(lambda rho_: iapws1995.p(rho_, T) - PMIN,
PMIN/(iapws1995.R*T))
# Determine the maximum density. For Tt < T < Tc use the liquid-vapor
# saturation density from IAPWS 1992; otherwise solve for it using an
# estimate from the ideal gas law (the extra factor of 1.5 helps avoid
# convergence problems around the critical density).
if iapws1995.Tt < T < iapws1995.Tc:
rhomax = iapws1992.rhosat_vapor(T)
else:
pmax = iapws2011.psubl_ice_Ih(T) if T < iapws1995.Tt else PMAX
rhoest = pmax/(iapws1995.R*T)*1.5
# pylint: disable=cell-var-from-loop
rhomax = newton(lambda rho_: iapws1995.p(rho_, T) - pmax, rhoest)
# Get the densities and pressures